QUESTION $1.$

The table below provides forecasts of possible returns of a stock of KdB PLC during the coming year. The forecasts are based on five equally$-$likely possible state of the economy. A state of the economy might be a severe recession, or a depression, or moderate growth in the economy

State of the economy probability Possible rates of return

$10\mathrm{.}200\mathrm{.}10$

$20\mathrm{.}200\mathrm{.}004$

$30\mathrm{.}20-0\mathrm{.}09$

$40\mathrm{.}200\mathrm{.}20$

$50\mathrm{.}200\mathrm{.}05$

Required: Compute the following: $-$

a$)$ Expected return of the stock

b$)$ Variance and standard variation of the stock$$s returns

QUESTION $2$

ABC Plc$.$ holds a portfolio of two assets which are asset X and Y

state probability Rate on return on X Rate of return on Y

$1.0\mathrm{.}200\mathrm{.}100\mathrm{.}03$

$2.0\mathrm{.}200\mathrm{.}04-0\mathrm{.}08$

$3.0\mathrm{.}20-0\mathrm{.}090\mathrm{.}07$

$4.0\mathrm{.}200\mathrm{.}200\mathrm{.}12$

$5.0\mathrm{.}200\mathrm{.}050\mathrm{.}21$

Required

$($a$)$ Explain the concept of weighted return of the portfolio

$($b$)$ Suppose that an investor invests $60\%$ of his money in asset X and $40\%$ in Asset Y; that is the portfolio weight are $60\%$ and $40\%$ respectively. Compute the expected return for portfolio

QUESTION $3$

Malombe LTD holds a portfolio of two assets A and B$.$ Suppose that each asset makes up $50\%$ of the total value of the portfolio. The expected return and standard deviation for assets A are$10\%$ and $0\mathrm{.}3,$ and for Assets B$,25\%$ and $0\mathrm{.}60,$ respectively.

Required

Calculate the expected returns and standard deviation of the portfolio on the following cases.

a$)$ Correlation coefficient is $+1$

b$)$ Correction coefficient is $0$ and

c$)$ Correlation coefficient is $-1$

QUESTION $4$

Mr Ikraam is a business man whose business are located in Dar es salaam city center. For as long period Ikraam has been hearing about capital market and has even attended some of the seminars on investing in capital market. Despite the vast information that Ikraam has on operation of capital market, he has not yet invested in any of the product traded in local stock exchange and the reason being lack of enough knowledge on choosing the profitable investment in the market. Recently one of the Ikraam friends who is a financial analyst advised Ikraam to consider the two shares which are traded in the local stock exchange that are considered to be more profitable.

The following information on the shares were obtained:

Alpha Shares Beta Shares

Annual investment return Probability of occurrence Annual investment return Probability of occurrence

$12\%0\mathrm{.}410\%0\mathrm{.}3$

$24\%0\mathrm{.}520\%0\mathrm{.}6$

$18\%0\mathrm{.}117\%0\mathrm{.}1$

The financial analysis has indicated that Ikraam should invest in both investment in order to optimize return and risk. The analyst calculated the co$-$efficient of correlation between the two shares which is $+0\mathrm{.}75$ and the financial analysis has conviced Ikraam to invest TZS $1,200,000$ in Alpha shares and TZS $800,000$ in Beta shares.

The analysis has established that the return on government bond is $4\%$ while the market has a return of $10\%$ and risk of $6\%.$

Required

i$.$ Estimate the expected return of each share and that of the proposed portfolio

ii$.$ Estimate the beta of the portfolio assuming that it is efficient according to the capital Asset pricing model $($CAPM$)$

QUESTION $5$

ILHAM LTD is an investment fund whose major holdings are its stocks and bonds acquired in various companies listed at the DSE. The company has recently acquired shares issued by Vodacom PLC which pays dividend of TZS $535$ to its shareholders. The shares have a beta factor of $1\mathrm{.}2.$ The risk$-$free rate of return and the market return are $15\%$ and $20\%$ respectively.

Required

I. Explain the concept of $$beta factor of portfolio$$

ii$.$ Calculate the return on the shares

QUESTION $6$

DP World limited intends to invest its surplus fund in shares of Tanzania Breweries limited $($TBL$)$ with the following return expectation.

Economic condition probability Share return

boom $0\mathrm{.}2040\%$

average $0\mathrm{.}6015\%$

recession $0\mathrm{.}20-10\%$

Required

I. Distinguish between $$required rate of return$$ and $$expected rate return$$

ii$.$ Using the coefficient of variation, assess the risk level associated with the investment

QUESTION $7$

Explain briefly what you understand by the following terms:

i$.$ Systematic risk

ii$.$ Unsystematic risk

iii. Optimal weight of portfolio

iv$.$ Diversification